Bresnan will join the Bears initially on a loan deal, subject to clearance from the England and Wales Cricket Board (ECB), which covers the remainder of the 2020 county season.
The club also announced pay-cuts across all sections of the staff to protect its long-term well being and stability.
Dent has been club captain for two full seasons and is one of Gloucestershire's longest-serving players despite just being 29.
Lyon joins Cheteshwar Pujara (Gloucestershire) and Michael Neser (Surrey) as the third overseas player in the Championship to have his contract cancelled for the upcoming season in the wake of coronavirus pandemic.
Murali Vijay featured in three Specsavers County Championship matches for Essex last season, scoring over 320 runs at an average of 64.60.
The 30-year-old Indian will replace South Africa batsman Aiden Markram, who will end his stint with Hampshire at the conclusion of the Royal London One-Day Cup group-stage.
On Wednesday, the Indian captain has been ruled out from participating in English County Championship due to a neck injury, suffered during the 11th edition of IPL.
New Delhi: Cheteshwar Pujara will be playing for Derbyshire this season while Varun Aaron is also keen on plying his trade in the county circuit but Ishant Sharma, the seniormost bowler of the Indian Test
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